Predictive Modeling and Analysis 8-1

 Logic-Driven Modeling  Data-Driven Modeling  Analyzing Uncertainty and Model Assumptions  Model Analysis Using Risk Solver Platform 8-2

 Predictive modeling is the heart and soul of business decisions.  Building decision models is more of an art than a science.  Creating good decision models requires: - solid understanding of business functional areas - knowledge of business practice and research - logical skills  It is best to start simple and enrich models as necessary. Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-3

Example 8.1 The Economic Value of a Customer  A restaurant customer dines 6 times a year and spends an average of $50 per visit.  The restaurant realizes a 40% margin on the average bill for food and drinks.  Annual gross profit on a customer = $50(6)(0.40) = $120  30% of customers do not return each year.  Average lifetime of a customer = 1/.3 = 3.33 years  Average gross profit for a customer = $120(3.33) = $400  OR Average gross profit for a customer = $120/.3 = $400 Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-4

Example 8.1 (continued) The Economic Value of a Customer V = value of a loyal customer R = revenue per purchase F = purchase frequency (number visits per year) M = gross profit margin D = defection rate (proportion customers not returning each year) Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-5

Example 8.2 A Profit Model Develop a decision model for predicting profit in face of uncertain demand. Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-6 Figure 8.1 P = profit R = revenue C = cost p = unit price c = unit cost F = fixed cost S = quantity sold D = demand Q = quantity produced

Example 8.2 (continued) A Profit Model Cost = fixed cost + variable cost C = F + cQ Revenue = price times quantity sold R = pS Quantity sold = Minimum{demand, quantity sold} S = min{D, Q} Profit = Revenue − Cost P = p*min{D, Q} − ( F + cQ) Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-7

Example 8.2 (continued) A Profit Model p = $40 c = $24 F = $400,000 D = 50,000 Q = 40,000 Compute: R = p*min{D,Q} = 40(40,000) = 1,600,000 C = F + cQ = 1,360,000 = 400, (40,000) P = R − C = 1,600,000 – 1,360,000 = $240,000 Logic-Driven Modeling Figure 8.2a Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-8

Example 8.2 (continued) A Profit ModelA Profit Model Logic-Driven Modeling Figure 8.2a Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-9 Figure 8.2b

Example 8.3 New-Product Development  Moore Pharmaceuticals needs to decide whether to conduct clinical trials and seek FDA approval for a newly developed drug. Estimated figures:  R&D cost = $700 million  Clinical trials cost = $150 million  Market size = 2 million people  Market size growth = 3% per year Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-10

Example 8.3 (continued) New-Product Development Additional estimated figures  Market share = 8%  Market share growth = 20% per year (for 5 years)  Revenue from a monthly prescription = $130  Variable cost for a monthly prescription = $40  Discount rate for net present value = 9% Moore Pharmaceuticals wants to determine net present value for the next 5 years and to determine how long it will take to recover fixed costs. Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-11

Example 8.3 (continued) New-Product Development Logic-Driven Modeling Figure 8.3b Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-12

Example 8.3 (continued) New-Product Development Logic-Driven Modeling Figure 8.3a Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-13 Profitable in 4 th year NPV = $185 million

Single-Period Purchase Decisions  One-time purchase decisions often must be made in the face of uncertain demand. Newsvendor Problem: How many newspapers to purchase each day?  C = cost to purchase a newspaper  Q = number of newspapers the vendor purchases  D = number of newspapers demanded  R = revenue from selling a newspaper  S = salvage value of unsold newspapers  Net profit = R(min{Q,D}) + S(max{0,Q − D}) − CQ Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-14

Example 8.4 A Single-Period Purchase Decision Model Net profit =18(min{Q,D}) + 9(max{0,Q − D}) − 12Q Logic-Driven Modeling Figure 8.4 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-15

Example 8.5 A Hotel Overbooking Model  A popular resort hotel has 300 rooms.  The room rate is $120 per night.  Reservations can be cancelled by 6:00 p.m.  Cost of overbooking is $100 per occurrence. Determine net revenue on the rooms.  Q = 300, P = 120, C = 100  D = Reservations − Cancellations  Net revenue = P(min{300,D}) − C(max{0,D − Q}) = 120(min{300,D}) − 100(max{0,D − 300}) Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-16

Example 8.5 (continued) A Hotel Overbooking Model Net revenue = 120(min{300,D}) − 100(max{0,D − 300}) Logic-Driven Modeling Figure 8.5 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-17

Example 8.6 A Retirement-Planning Model  Start work at age 22, earning $50,000 per year.  Expect a salary increase of 3% per year.  Required to contribute 8% to retirement.  Employer contributes 35% of that amount.  Expect an annual return of 8% on the portfolio. Determine the value of the retirement account when the employee is 50 years old. Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-18

Example 8.6 (continued) Retirement-Planning Model  Salary = 1.03(previous year’s salary)  Employee contribution = 0.08(salary)  Employer contribution = 0.35(employee contrib.)  Value of account = 1.08(previous value) + employee contribution + employer contribution Logic-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-19 Figure 8.6a

Example 8.6 (continued) Retirement Planning Model Logic-Driven Modeling Figure 8.6b Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-20 Value at 50 years old = $751,757 Value at 22 years old = $5,400

Example 8.7 Modeling Retail Markdown Pricing Decisions  In the spring, a department store introduces a new line of bathing suits that sells for $70.  The store purchases 1000 of these bathing suits.  During the prime selling season, the store sells an average of 7 units per day at full price (40 days).  On 10 sale days, the price is discounted 30% and sales increase to 32.2 units per day.  Around July 4 th, the price is marked down 70% to sell off remaining inventory.  Determine total revenue from the bathing suits. Data-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-21

Example 8.7 (continued) Modeling Retail MarkdownRetail Markdown Pricing Decisions Data-Driven Modeling Figure 8.7 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-22 Assume a linear trend model between sales and price: daily sales = a – b(price) 7 = a – b(70) 32.2 = a – b(49) Daily sales = 91 – 1.2(price)

Example 8.7 (continued) Data-Driven Modeling Figure 8.7 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-23 Revenue from full retail sales = units sold * days * price = (7)*(40)*(70) = $19,600 Revenue from sale weekends = (32.2)*(10)*(49) = $15,778 Revenue from clearance sales = leftovers * price = (1000 − 7(40) − 32.2(10))*(21) = (398)(21) = $8,358

Example 8.7 (continued) Modeling Retail Markdown Pricing Decisions Data-Driven Modeling Figure 8.7 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-24 Total revenue = $43,736

Modeling Relationships and Trends in Data Create charts to better understand data sets. For cross-sectional data, use a scatter chart. For time series data, use a line chart. Consider using mathematical functions to model relationships. Data-Driven Modeling Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-25

Excel Trendline tool Click on a chart  Chart tools  Layout  Trendline Choose a Trendline. Choose whether to display equation and R-squared. Data-Driven Modeling Figure 8.8 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-26 R-squared values closer to 1 indicate better fit of the Trendline to the data.

Example 8.8 Modeling a Price-Demand Function Data-Driven Modeling Figure 8.9 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-27 Linear demand function: Sales = (price)

What-If Analysis Spreadsheet models allow you to easily evaluate what-if questions. How do changes in model inputs (that reflect key assumptions) affect model outputs? Systematic approaches to what-if analysis make the process easier and more useful. Analyzing Uncertainty and Model Assumptions Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-28

Data Tables  Data Tables summarize the impact of one or two inputs on a specified output.  Excel data table types: One-way data tables – for one input variable Two-way data table – for two input variables To construct a data table:  Data  What-If Analysis  Data Table Analyzing Uncertainty and Model Assumptions Figure 8.14 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-29

Example 8.11 A One-Way Data Table for Uncertain Demand Analyzing Uncertainty and Model Assumptions Figure 8.14 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-30 Create a column of demand values (column E). Enter =C22 in cell F3 (to reference the output cell). Highlight the range E3:F11. Choose Data Table. Enter B8 for Column input cell. (tells Excel that column E is demand values) Figure 8.15a Data Table tool computes these values

Example 8.11 (continued) A One-Way Data Table for Uncertain Demand Analyzing Uncertainty and Model Assumptions Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-31 Figure 8.15b The Data Table tool computes the profit values in column F (below $240,000).

Example 8.12 One-Way Data Tables with Multiple Outputs Create a second output, revenue. Analyzing Uncertainty and Model Assumptions Figure 8.15 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-32 Enter =C15 in cell G3. Highlight E3:G11. Choose Data Table Proceed as in the previous example. Excel computes the revenues values.

Example 8.13 A Two-Way Data Table for the Profit Model Evaluate the impact of both unit price and unit cost Analyzing Uncertainty and Model Assumptions Figure 8.17a Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-33 Create a column of unit prices (F5:F15). Create a row of unit costs (G4:J4). Enter =C22 in cell F4. Select F4:J15. Choose Data Table. Data Table tool computes these cell values. Enter B6 for Row input cell. Enter B5 for Column input cell.

Example 8.13 (continued) A Two-Way Data Table for the Profit Model Analyzing Uncertainty and Model Assumptions Figure 8.17b Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-34

Goal Seek Goal Seek allows you to alter the data used in a formula in order to find out what the results will be.  Set cell contains the formula that will return the result you're seeking.  To value is the target value you want the formula to return.  By changing cell is the location of the input value that Excel can change to reach the target. Analyzing Uncertainty and Model Assumptions Figure 8.21 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-35

Example 8.15 Finding the Breakeven Point in the Outsourcing Model (using Goal Seek) Find the value of demand at which manufacturing cost equals purchased cost Set cell: B19 To value: 0 By changing cell: B12. Analyzing Uncertainty and Model Assumptions Figure 8.21 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall Figure 8.22 The breakeven volume is 1000 units.

Tornado Chart Shows the impact that variation in a model input has on some output while holding all other inputs constant. Shows which inputs are the least and most influential on the output. Helps you select the inputs that you would want to further analyze. Model Analysis Using Risk Solver Platform Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-37

Example 8.17 Creating a Tornado Chart in Risk Solver Platform Model Analysis Using Risk Solver Platform Figure 8.28 Copyright © 2013 Pearson Education, Inc. publishing as Prentice Hall 8-38 Profit Model Select cell C22. Parameters Identify A 10% change in unit price (B5) affects profit the most. Next is unit cost (B6).